INFLUENCE  OF  GRAIN  SIZE  UPON  THE  STRENGTH 
OF  STEEL  UNDER  REPEATED  STRESS 

BY 

ROGER  MOORE  BOND 
A.  B.  Monmouth  College,  1920 


THESIS 

Submitted  in  Partial  Fulfillment  of  the  Requirements  for  the 

Degree  of 

MASTER  OF  SCIENCE 
IN  CHEMISTRY 

IN 

THE  GRADUATE  SCHOOL 
OF  THE 

UNIVERSITY  OF  ILLINOIS 


1921 


Digitized  by  the  Internet  Archive 
in  2016 


https://archive.org/details/influenceofgrainOObond 


U NIVERSITY  OF  ILLINOIS 


THE  GRADUATE  SCHOOL 


_ June  four "Gii,  iq?  1 


I HEREBY  RECOMMEND  THAT  THE  THESIS  PREPARED  UNDER  MY 


SUPERVISION  BY 


ROC!-1?'0  UOOTE  BOOT) 


ENTITLED  TWLTOTmS  nv  GRAT'I  HT7.E  TTPfflT  TTTTg 


STRENGTH  OF  STEEL  HOTER  ^RTEATET)  STRESS 


BE  ACCEPTED  AS  FULFILLING  THIS  PART  OF  THE  REQUIREMENTS  FOR 


THE  DEGREE  OF 


MASTER  OF  SOIBWOE  IN  CHEMISTRY 

gJ.  Lav. 


W* 


4 

A. 


In  Charge  of  Thesis 


— 


Head  of  Department 


Recommendation  concurred  in* 


Committee 


on 


Final  Examination* 


*Required  for  doctor’s  degree  but  not  for  master’s 


/!  n q 
O'O 


ACKNOWLEDGEMENT 


Thanks  are  due  to  Professor  Herbert 
Fisher  Moore,  of  the  Engineering  Experiment 
Station,  and  to  Doctor  Willis  Sumner  Putman, 
of  the  Applied  Chemistry  Department,  for  their 
friendly  supervision  and  their  many  suggestions. 
I am  especially  indebted  to  Doctor  Putman  for 
his  exacting  personal  supervision  and  his 
patient  efforts  to  teach  me  something  of  the 
difficult  art  of  micro-photography. 


TABLE  OF  CONTENTS 


I.  Historical  Sketch.  . 1 

II.  Introductory  Material,  ......  10 

III.  The  Problem 14 

IV.  Theoretical  Solution  .......  14 

V.  Method  of  Attack 16 

A.  Selection  of  Specimens.  .......  16 

B.  Method  of  Heat-Treatment.  ......  1? 

C.  Testing  of  Specimens 18 

D.  Study  of  Microstructure.  . 20 

E.  Grain  Count.  21 

VI.  Conclusions .22 

VII,  Appendix 24 

A.  Tables  of  results  of  tests 24 

B.  Photomicrographs 25 

C.  Curves.  39 

D.  Bibliography 40 


INFLUENCE  OF  GRAIN  SIZE  UPON  THE  STRENGTH 


OF  STEEL  UNDER  REPEATED  STRESS 
HISTORICAL 

The  first  investigation  of  the  problem  of  fatigue  in 
metals  was  begun  by  August  Wohler^,  "Ober-maschinenmeister " on 
the  Royal  Lower  Silesia-Brandenbur g railway  in  1860.  The  purpose 
was  primarily  to  solve  problems  in  the  design  of  oar- axles  and  of 
members  of  iron  bridges,  but  the  investigation  was  so  thorough  and 
basic  that  it  has  served  as  a model  for  all  later  investigators 
and  as  material  for  speculation  to  everyone  with  a new  idea  for 
endurance  limit  formulae.  It  included  static  and  endurance  tests 
in  torsion,  tension  and  transverse  stress  with  different  materials 
and,  in  some  cases,  different  shapes.  For  the  transverse  stress  he 
used  repeated  loading  and  rotating  beam  machines.  The  former  was 
a simple  beam  and  the  latter  a cantilever  beam.  The  rotating  beam 
gave  considerable  trouble  because  the  specimens  were  driven  into 
place  and  frequently  broke  in  the  sockets.  The  speed  was  about 
seventy-two  revolutions  per  minute,  and  one  pieoe  was  run 
132,250,000  cycles  without  rupture.  Bars  under  load  which  were  run 
intermittently  broke  after  fewer  repetitions  than  those  which  had 
been  run  3teadily.  Re-entrant  angles  made  the  piece  much  weaker 
and  a fillet  improved  the  strength  at  a collar.  Merriman  gives 
this  summary  of  Wohler's  investigation: 

1.  By  repeated  applications  of  stress,  rupture  may  be 
caused  by  a unit-stress  far  less  in  value  than  the 
ultimate  strength  of  the  material. 

2.  The  greater  the  range  of  stress,  the  less  is  the  unit- 
stress  required  to  produoe  rupture  after  an  enormous 


-2- 


number  of  applications. 

3.  When  unit  stress  in  a bar  varies  from  zero  up  to  the 
elastic  limit,  the  number  of  applications  required  to 

rupture  it  is  enormous. 

4.  A range  of  stress  from  tension  into  compression  or  vice 
versa  produces  rupture  with  a less  number  of  applications 
than  the  same  range  in  stress  of  one  sign  only. 

5.  When  the  range  in  stress  in  tension  is  equal  to  that  in 
compression,  the  unit-stress  that  produces  rupture  after 
an  enormous  number  of  repetitions  is  greater  than  one- 
half  the  elastic  limit. 

’’Except  in  fast-moving  machinery,  this  great  number 
(40, COO, COO)  would  seldom  be  exceeded  during  the  natural 
life  of  the  piece.”  Wohler. 

Wohler  concluded  that  there  should  be  two  factors  of  safety  in 
design  of  machines:  one  a proportion  between  steady  load  and 

’’limit  of  fracture”,  and  one  a factor  for  strain  or  oscillation 

•TL 

of  load.  Bauschinger ,J  later  conducted  investigations  which  'were 
characterized  by  the  delicate  accuracy  of  his  measurements  and 
decided  that  the  endurance  limit  of  material  depended  upon  the 
"natural  elastic  limit”.  From  the  work  of  these  two  men  Gerber 6 
and  Weyrauch  and  Launhardt^  evolved  formulae  for  working  stress. 

The  next  advance  in  the  study  of  fatigue  phenomena  came 
about  1898  when  the  microscopic  study  of  metals  began  to  be 
rather  wide-spread.  Ewing;  end  Rosenhain^  subjected  pieces  of 
metal  to  strain  in  a testing  machine  mounted  on  a microscope  and 
established  fairly  good  proof  of  the  statement  that  the  metal 
yi&ded  by  a slipping  of  the  crystals  composing  its  structure  along 
lines  of  cleavage  in  the  crystals.  These  slips  were  indicated 
on  the  polished  surface  of  the  metal  by  ridges  or  ’’slip  bands.” 
Repeated  stress  increased  the  number  of  the  slip  bands  until  the 


LV 


-3- 


metal  gave  way  by  a rupture  which  extended  through  the  crystal. 
Repolishing  the  surface  destroyed  the  slip  bands  and  their  exist- 
ence w^s  challenged  by  Osmond  and  Cartaud.  Rosenhain®^  by  electro- 
plating a polished  surface  containing  slip  bands,  was  able  to  make 
a cross  section  of  a series  of  them  and  show  beyond  shadow  of  doubt 
that  they  were  formed  by  the  slipping  of  parts  of  the  crystals 
along  cleavage  planes  which  exist  in  all  crystals. 

About  the  yes„r  1898  a great  advance  in  metallurgy  was  in 
progress.  In  1888  Mushet  introduced  the  first  alloy  steel  to  gain 
wide  use,  a tungsten  (w self -hardening")  tool  steel. ^ Fifteen  years 
later  chromium  came  into  use  as  an  alloying  element  and  in  1882 
R.  A.  Hadfield  discovered  how  to  produce  a very  valuable  alloy 
steel  containing  from  ”7  to  30”  percent  manganese.  In  18S9  Taylor 
and  White  introduced  high  speed  tool  steel.  These  advances  did  not 
change  Wohler's  tests,  with  his  rotating  beam  turning  seventy- two 
revolutions  per  minute.  Again,  the  endurance  limit  of  a piece  is 
worth  knowing,  for  it  does  not  always  coincide  with  the  elastic 
limit  as  proposed  by  Bauschinger  and  the  elastic  limit  is  a very 
elusive  quantity,  whereas  accurate  knowledge  of  the  endurance  limit 
makes  saving  of  weight  or  greater  margin  of  safety  possible.  The 
early  methods  of  running  endurance  tests  were  very  slow  and  their 
value  was  disputed.  Andrews®  cites  a long  list  of  railway  and 
steamship  accidents  which  were  rather  serious  and  were  plainly  due 
to  defects  in  steel  axles,  propellor  shafts  or  other  vital  parts. 

He  considered  the  failures  due  almost  entirely  to  flaws,  sulphide 
streaks,  and  other  enclosed  impurities  inherent  in  the  steel,  and 

put  his  faith  in  wrought  iron.  Fatigue  investigations  were  opened 
along  with  the  microscopic  study  of  the  metal  which  he  recommended. 


-<±- 


These  began  to  cover  a wider  field  than  the  earlier  ones.  The 
great  desideratum  was  and  is  a method  by  which  the  endurance  limit 
of  a steel  may  be  determined  in  a reasonable  time  and  without  pro- 
hibitive expense.  The  uncertainty  as  to  the  precise  nature  of  the 
phenomenon  and  the  doubt  in  the  minds  of  the  investigators  of  the 
influence  of  certain  factors,  such  as  speed,  rest,  range  of  stress, 
shock,  temperature,  form,  chemical  composition  and  micro-structure, 
distribution  of  stress,  previous  cold-work,  annealing, ( of  thS  last 
two  microstructure  is  -the  result)  . This  uncertainty  and  this 
doubt  caused  a great  variety  of  tests  to  be  attempted  and  a great 
many  theories  to  be  advanced,  with  consequent  confusion. 

The  outstanding  work  of  the  period  1896-^.911  was  that  done 
in  England  by  Reynolds  and  Smith2^,  Stanton  and  Bairs tow^J  on  the 
"throw  testing  machine"  designed  by  Reynolds  originally.  The  idea 
was  that  the  rotating  beam  machines  stressed  the  surface  fibers 
most  where  the  machine  they  used  employed  alternate  simple  tension, 
and  compression  for  it  depended  upon  the  inertia  of  a cross-head 
actuated  by  a crank  and.  connecting  rod.  When  the  stress  was  great- 
est, as  the  motion  of  the  crosshead  was  passing  through  zero,  the 
friction  of  the  cross-head  became  negligible.  The  force  of  inertia 
varies  as  the  square  of  the  speed  and  the  stress  could  be  calculat- 
ed with  some  accuracy.  The  speed  employed  was  800  reversals  per 
minute  for  Stanton  and  Bairstow's  work,  1000-2000  reversals  per 
minute  for  Reynolds  and  Smith’s.  The  range  of  stress  was  a little 
lower  for  the  tests  of  Reynolds  and  Smith,  perhaps  on  account  of 
the  speed  which  would  influence  the  friction  of  the  cross-head. 

The  others  found  that  the  speed  was  not  an  important  factor  but 


that  the  endurance  limit  was  directly  proportional  to  the  percent- 
age of  carbon  in  the  steel  (which  was  not  heat-treated),  and  that 
rapidity  of  charge  of  section  was  vital.  Unwin  tabulates  a test 
made  by  Stanton  and  Bairstow  on  three  bars  of  Swedish  Bessemer 
steel  which  had  not  been  broken  by  mors  than  a million  and  a 
quarter  reversals  at  the  endurance  limit.  The  bars  were  broken 
by  static  stress,  one  by  compression,  two  by  tension,  and  the 
elastic  limits  corresponded  to  the  range  in  stress,  though  both 
the  limit  for  tension  and  that  for  compression  had  been  lowered. 
Unwin®  cites  this  as  an  example  Gf  Bauschinger ’ s suggestion  that 
if  the  range  of  stress  fell  within  the  "natural  elastic  limits" 
the  number  of  repetitions  would  be  unlimited.  The  suggestion 
would  be  valuable  if  the" natural  elastic  limits"  could  be  obtained 
in  any  way  except  by  endurance  tests.  Turner  attempted  to 
attain  the  same  result  by  annealing  the  metal  and  Moore  and 
Putnam  found  that  the  curve  of  a cold-rolled  steel  intersected 
that  of  the  same  steel  which  had  been  annealed.  The  endurance 
limit  can  be  altered  by  annealing,  however,  the  theory  of 
Bauschinger  was  purely  empirical.  It  has  not  been  found  practic- 
able for  determining  endurance  limits,  though  a piece  might  be 
run  a few  million  revolutions  under  alternating  stress  and  then 
broken  under  static  stress  if  the  theory  were  fundamentally  true. 

Some  of  the  most  valuable  work  of  the  period  was  that  of 
Ewing  and  Rosenhain^,  Ewing  and  Humfrey^,  and  Rosenhain.  The 
first-named  demonstrated  the  manner  of  failure  of  a metal:  slip 
along  the  cleavage  planes  of  the  crystals  which  compose  it.  The 
second-named  showed  that  a repetition  of  stress  produced  fracture 


- ... 


. • • 


w* 


—6— 

by  extending  and  uniting  of  slip-bands.  Stanton  and  Bair stow 
applied  the  results  of  the  former  researches  to  the  endurance  tests 
of  steel  and  showed  that  the  results  were  valid.  They  also  showed 
that  in  high  carbon  steels  which  have  been  annealed  the  path  of 
fracture  follows  the  ferrite  grains  rather  than  the  pearlite. 

This  is  the  foundation  of  the  met alio graphic  study  of  fatigue. 

9 

Andrews  gives  some  excellent  photomicrographic  studies  of  steels 
which  appear  to  have  broken  by  fatigue  and  illustrate  the  fact 
that  fatigue  failure  may  take  place  after  a few  hundred  repetitions 
of  a stress  which  exceeds  the  endurance  limit. 

13 

The  investigation  of  Eden,  Rose  and  Cunningham  ‘ in  1911 
seems  to  mark  a change  in  the  spirit  of  attack.  They  treat  the 
problem  as  one  of  commercial  importance  demanding  systematic 
solution.  They  used  a simple  rotating  beam  instead  of  a canti- 
lever beam  and  they  plotted  their  results  on  logarithmic  paper 

sc  that  their  curves  were  straight  lines  and  more  easily  dealt 

28 

with.  Upton  and  Lewis  recommended  a short  time  test  machine 
on  a different  principle  but  with  the  definite  idea  of  intro- 
ducing endurance  tests  on  a large  scale,  and  overcoming  the 
practical  difficulties.  One  advance  of  Eden,  Rose  and  Cunningham 
was  the  high  speed  which  they  were  able  to  use,  although  excessive 
vibration  ruined  some  tests.  They  studied  the  effect  of  speed, 
rest,  vibration  and  annealing.  They  ran  a series  of  specimens 
with  highly  polished  surface  and  found  that  the  scratch  of  a 
needle  on  that  surface  would  lower  the  endurance  strength  and 
throw  the  piece  off  the  stress  curve.  They  experimented  with  the 
form  of  test-piece  but  the  form  they  used  most,  had  a minimum 
section  between  the  bearings  of  the  load  to  induce  fracture 


-7- 

where  the  stress  could  be  more  easily  computed.  Ir.  the  present 

investigation  the  same  idea  has  been  employed  and  improved  upon  so 

that  failure  rarely  takes  place  except  in  the  reduced  section 

which  may  have  a known  area  and  a highly  polished  surface  which  is 

not  liable  to  damage  in  setting  up  the  machine.  The  extensity  of 

their  investigation  was  due  to  the  higher  speed  which  permitted  the 

running  of  a comparatively  large  number  of  tests  and  which  did  not 

materially  affect  the  results.  There  had  been  other  attempts  to 

shorten  the  time  of  testing.  They  usually  tried  to  relate  endur- 

ande  limit  to  static  tests,  and,  as  Upton  and  Lewis  point  out,  ther 

is  no  known  relation  between  fatigue  and  tension.  The  logarithmic 

plotting  of  unit-stress  against  cycles  gave  a straight  line  for 

the  number  of  cycles  used  and  promised  the  possibility  of  obtaining 

a measure  of  endurance  strength  with  very  few  points.  Upton  and 

Lewis  recommended  high  stress  tests  to  locate  the  position  and 

4 

direction  of  the  line.  Rosenhain  points  out  that  the  curve 
demands  a considerable  number  of  points  and  cannot  be  accurately 
located  by  any  single  point. 

The  only  American  work  on  the  fatigue  of  metals  prior  to 
1S10  that  appears  in  the  literature  is  that  of  J.  E.  Howard  at  the 
Watertown  Arsenal  (1SS8-1910)  . Since  that  time  the  question  has 

occupied  a great  deal  of  attention  in  America.  In  1910  Professor 
Basquin  of  Northwestern  University  gave  a paper  on  the  "Exponential 
Law  of  Endurance  Tests"  before  the  American  Society  for  Testing 
Materials.  The  logarithmic  plotting  of  endurance  curves  appears 
to  be  due  to  him.  Moore  and  Seely30  gave  a logical  and  mathemat- 
ical development  of  the  whole  fatigue  theory,  which  'works  very 


-8- 

weil  except  that  it  throws  some  doubt  on  the  existence  of  an 
endurance  limit  which  later  tests  have  dispelled.  The  long  time 
tests  with  loads  below  a certain  amount,  run  an  enormously  greater 
time  for  a very  slightly  smaller  load,  and  the  curve  is  practically 
parallel  to  the  repetition  ordinate  even  when  it  is  plotted  on 
logarithmic  paper.  One  advance  from  this  theory  is  the  definite 
proof  that  the  endurance  limit  of  a material  is  apparent  when  a 
stress  has  been  found,  at  which  a given  specimen  will  run  about 
four  million  cycles  on  a rotating  beam  machine.  Stanton  and 
Eairstow  wer e content  with  specimens  which  ran  more  than  a million 
reversals  on  their  inertia  machine,  although  the  conditions  were 
not  very  like.  If  a piece  is  to  run  practically  to  infinity  the 
curve  must  become  parallel  to  the  axis  along  which  are  plotted 
the  number  of  reversals  of  stress.  The  curve  does  not  reach  this 
value  until  the  piece  is  capable  of  running  about  four  million 
repetitions  at  the  given  stress. 

In  the  last  five  years  America  has  come  to  the  front  in 
the  study  of  fatigue  in  metals.  The  problem  is  to  find  a method 
by  which  the  endurance  limit  of  metals  may  be  determined  as 
readily  and  cheaply  as  the  other  physical  properties  are  found  in 
modern  plants.  It  is  plain  that  different  metals  or  different 
steels  have  different  endurance  limits,  just  as  they  have 
different  elastic  limits,  ductility,  ultimate  strength,  coefficient 
of  expansion  or  electrical  conductivity.  The  difficulty  has  been 
that  the  endurance  limit  could  not  be  found  readily  and  that  it 
has  been  considered  cheaper  and  easier  to  use  heavier  parts  for 
structures  or  machines  than  the  limit  would  demand.  But  there 


. ■ v'  ’• 

I 


' • 


( ' . 


; 


i ' 


-9- 

is  a constantly  growing  demand  for  yet  lighter,  higher  speed 

machines.  The  automobile  and  the  air-plane  were  made  possible 

only  by  the  advance  in  knowledge  of  the  properties  of  the  metals. 

The  automobile  built  according  to  the  best  possible  designs  of 

fifty  or  less  years  ago  would  have  been  flimsy  or  immovable.  The 

bicycle  of  that  time  weighed  about  four  times  as  much  as  the 

modern  one  and  was  more  fragile.  The  air-plane  was  a topic  for 

humorists  until  an  exceedingly  light  and  powerful  engine  was 

evolved.  The  task,  in  the  words  of  Unwin,  is  "to  determine  the 

minimum  amount  of  material  and  the  best  disposition  of  it  in 

27 

machines  and  structures  to  secure  safety?  The  phenomenon  of 

fatigue  in  metals  was  brought  to  light  principally  by  German 

investigators,  Wohler,  Bauschinger,  Spangenberg,  Gerber,  Weyrauch 

and  Launhardt.  Much  of  the  theory  which  most  satisfactorily 

explains  it,  was  developed  by  English  engineers  and  metallurgists, 

Ewing,  Rosenhain,  Humfrey,  Stanton  and  Bairstow,  Arnold,  Strorneyer, 

Reynolds  and  Smith  and  others.  Americans  may  have  the  opportunity 

to  develop  the  application  of  fatigue  tests  to  the  point  where 

they  will  be  available  for  the  material  and  uses  which  demand  them. 

This  was  the  object  of  the  National  Research  Council  and  of  the 

Engineering  Foundation  when  they  arranged  for  a joint  investigatior 

1 s 

of  the  subject.  The  machine  designed  by  F.  M.  Farmer  , after  the 
suggestion  of  H.  F.  Moore,  is  much  more  practical  than  any  of  the 
earlier  machines  for  endurance  testing,  especially  on  a large 
scale.  The  report  of  the  Joint  Committee  in  the  Journal  of  the 
American  Sodiety  of  Mechanical  Engineers  in  Mechanical  Engineering 
for  September  1919  is  a very  complete  and  thorough  statement  of 


-10- 

the  various  aspects  of  the  problem  and  provides  assurance  that  it 
will  be  taken  up  from  every  angle  which  has  shown  signs  of 
promise  to  previous  investigators. 

II  INTRODUCTORY 

The  micro structure  of  metals  is  certainly  a determining 
factor  of  their  properties.  There  are  three  vital  points  in  the 
study  of  the  microstructure:  (l)  a means  of  comparing  the  structure 
(2)  a means  of  producing  various  structures  at  will,  .and  (3)  means 
of  testing  the  properties  of  the  metal  having  the  specified 
structure.  The  first  is  attained  by  the  microscope  and  camera 
combined  with  chemical  analysis.  The  second  may  be  reached  by  the 
aid  of  the  thermo-couple  of  LeChatelier  or  the  platinum  resistance 
pyrometer,  radiation  or  optical  pyrometers,  for  the  structure  is 
affected  most  by  temperature  and  accurate  means  of  measuring  high 
temperatures  is  vital.  The  testing  science  had  a beginning  at 
least  in  the  time  of  Galileo,  but  is  empirical  so  far  as  different 
materials  are  concerned.  Materials  were  classified  on  the 
locality  from  which  they  came  in  the  old  days.  Later  chemical 
analysis  became  the  fashion  but  was  unsatisfactory  because  a 
given  material  might  have  a certain  analysis  and  two  speciment  be 
opposite  in  properties.  Microstructure  seems  to  b e an  infinitely 
better  basis  for  classifying  the  results  of  tests  and  the  study 
as  such  has  been  developed  within  the  last  thirty  years,  by  such 
men  as  Osmond,  Rosenhain,  Stead,  Roberts-Aust en,  Roozeboom,  Howe, 
Saveur,  LeChatelier,  Carpenter,  Arnold,  Heyn,  Benedicks,  Martens 
and  Sorby . 


-11- 


The  factors  influencing  the  growth  of  the  crystalline 
grains  in  any  metal  have  been  given  a great  deal  of  attention. 
Ewing  and  Rosenhain  showed  that  the  crystals  of  lead  grow  at  room 
temperatures  though  not  unless  they  have  been  deformed  by  strain. 
They  explained  the  action  as  electrolytic.  The  "eutectic  cement” 
theory,  which  they  advanced,  stated  that  even  in  very  pure  metal 
there  was  enough  impurity  to  form  a eutectic  around  the  boundaries 
of  the  crystals.  Any  deformation  caused  contact  of  two  crystals 
and  thus  the  establishment  of  an  electrical  circuit,  which  by 
electrolysis  (from  the  difference  in  potential  between  the  con- 
tact  junction  and  the  solution  junction)  transferred  matter  from 
one  crystal  to  another.  The  theory  seemed  plausible  and  was 
beautifully  illustrated  by  an  experiment  with  lead,  but  has  not 

9 'Z 

been  generally  adopted  and  Rosenhain  and  Ewen  later  brought 

forth  some  experiments  of  metal  which,  they  claimed,  could  not 

have  enough  impurities  to  form  a eutectic.  Stead  performed  some 

5 

experiments  on  ferrite  in  1898  which  indicated  that  crystals  of 
iron  containing  less  than  0.15 $ carbon  would  grow  on  annealing 
below  the  critical  temperature.  Sauveur  gives  some  photographs 
on  0.05  ‘jo  carbon  steel  which  had  been  subjected  to  a stress  vary- 
ing in  intensity  throughout  the  section,  and  then  annealed  at  650° 
Centigrade  seven  hours,  before  it  was  photographed.  He  also  gives 
a test  by  C.  Chappell  with  a picture  of  brass  broken  by  tension 
and  annealed.  The  piece  was  tapered  toward  the  center  so  that 
the  unit  stress  varied  from  the  center  to  the  ends.  There  were 
three  zones  of  crystals.  Those  in  the  center  had  been  very 
severely  stressed  and  were  very  small  and  those  toward  the  end 


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which  had  been  very  slightly  stressed  were  smaller  yet.  Those  in 
the  center  were  very  large,  indicating  that  a critical  stress  was 

necessary  to  produce  growth. 

1 ? 

Carpenter  and  Elam  give  a highly  satisfactory  theory  of 
crystal  growth  and  a large  amount  of  evidence  to  substantiate  it. 
’’Crystal  growth,  ’’  they  say,  is  the  re-arrangement  of  certain 
crystals  in  a crystal  aggregate  to  conform  with  the  orientation  of 
certain  other  crystals  during  which  process  the  latter  increase 
in  size  by  the  addition  of  re-oriented  material  at  the  same  time 
as  the  former  decrease  in  size  by  the  same  amount.”  ’’Recrystal- 
lization” is  the  "complete  re-orientation  of  a crystal  or  a group 
of  crystals."  It  starts  from  new  centers,  is  c4uite  independent 
of  the  old  system  of  orientation,  is  characterised  by  a refined 
structure  and  is  complete  when  all  traces  of  the  old  system  dis- 
appear. The  alloy  which  they  used  to  demonstrate  the  manner  of 
crystal  growth  was  comparatively  easy  to  obtain  and  to  study. 

A picture  of  a specimen  which  was  prepared  in  this  laboratory  is 
shown  in  this  thesis.  The  theory  is  that  there  are  three  factors 
which  are  concerned  with  the  growth  of  crystals  in  any  metal. 

These  are  time,  temperature,  and  amount  of  plastic  deformation. 
There  can  be  no  growth  in  which  all  these  are  not  included,  though 
in  general,  the  last  has  been  slighted.  They  proved  that  metal 
which  has  not  been  plastically  deformed  does  not  increase  in 
grain  size  and.  that  for  equal  time  and  equivalent  temperature  the 
amount  of  growth  is  determined  by  plastic  deformation  of  the 
crystals.  For  the  same  deformation  the  amount  of  growth  is 
determined  by  the  time  and  temperature.  The  explanation  for 


-13- 


Chappell's  experiment  is  that  the  crystals  in  the  center  had  been 
strained  enough  to  start  re-crystallization,  while  those  on  the  end 
had  not  been  strained  enough  to  start  growth  and  those  between  had 
been  strained  sufficiently  to  grove.  If  the  piece  had  been  anneal- 
ed at  a lower  temperature  it  would  have  shown  a larger  area  of 
unchanged  crystals,  and  a smaller  area  of  recrystallization  while 
the  area  of  growth  would  have  been  about  the  same.  If  it  had  been 
annealed  at  a higher  temperature  the  area  of  r eery stall iaat ion 
would  have  been  larger.  "The  higher  the  temperature,  the  less 
the  deformation  required  to  produce  crystals  of  the  maximum  size 
obtainable  at  that  temperature." 

There  seems  to  have  been  ho  formal  investigation  of  the 

fatigue  strength  of  the  metals  on  the  basis  of  grain  size,  though 

the  authorieies  who  mention  the  subject  of  this  research  are 

positive  that  the  endurance  strength  decreases  as  the  grain  size 

increases,  for  example,  Upton'  in  Materials  of  Construction,  says, 

(P.  112)  "in  the  case  of  the  piece  failing  in  service  when  similar 

pieces  stand  up,  the  original  crystal  size  of  the  piece  which 

25 

failed  was  larger."  In  the  report  of  the  Joint  Committee'''  , which 

1 n 

suggested  the  problem,  Rosenhain  is  quoted: 

"The  question  then  arises  whether  the  increased  size  of 
crystals  produced  in  a simple  metal  by  prolonged  heating  is  in- 
jurious or  otherwise,  so  far  as  the  useful  properties,  and  more 
especially  the  mechanical  properties  of  the  metal  are  concerned. 
There  can  be  little  doubt  that  within  reasonable  limits  the 
mechanical  properties  of  a simple  metal  are  better,  the  smaller 
the  constituent  crystals  of  which  it  is  built  up.  Under  the 
tensile  test,  coarseness  of  structure  usually  results  only  in  a 
slightly  lowered  yield  point,  while  the  ultimate  stress  and  the 
elongation  are  little  impaired,  although  the  reduction  of  area 
at  fracture  is  sometimes  markedly  less.  On  the  other  hand,  under 
both  shock  and  fatigue  tests,  a coarse  structure,  even  in  a 
simple  metal  gives  unsatisfactory  results." 


1 


—14— 

III.  THE  PROBLEM 

The  problem  of  this  research  is  simply  to  produce  a uniform 
grain  size  in  several  groups  of  specimens  of  the  same  steel,  so 
that  the  groups  will  be  alike  except  for  grain  size,  and  to  deter- 
mine the  stress  at  which  each  group  will  withstand  an  infinite 
number  of  repetitions  of  the  stress.  The  results  should  display 
the  relation,  if  any,  between  grain  size  and  endurance  strength. 

IV.  THEORETICAL  SOLUTION 

It  has  been  stated  that  repeated  stress  causes  deformation 
of  the  crystals  which  compose  the  metal  through  the  formation  of 
slip-bands  in  the  crystals.  The  pictures  by  Professor  Moore 
demonstrate  this  vividly  . He  has  obtained  motion  pictures  of  the 
polished  surface  of  a specimen  which  was  being  bent  alternately 
back  and  forth.  The  rate  of  bending  was  slow  enough  to  permit 
observation,  but  the  straining  of  the  metal  was  so  severe  that  a 
crack  was  developed.  The  deformation  of  the  crystals  was  striking 
for  they  shifted  like  an  old  wooden  box,  but  mor § striking,  because 
otherwise  invisible,  was  the  action  of  the  boundaries.  They 
appeared  to  be  perfectly  elastic  and  the  crack  developed  in  the 
crystal  proper. 

When  the  stress  is  so  great  that  the  crystals  are  deformed 
a quantity  of  energy  must  be  transformed  into  heat,  for  the  move- 
ment of  the  slip-planes  certainly  involves  friction)  but  if  the 
crystal  bounder ies  are  elastic  they  would  not  cause  any  heating; 
effect,  The  motion  caused  by  stress  below  that  necessary  to  deform 
a considerable  number  of  crystals  would  not  cause  the  evolution  of 


-15- 


heat  and  should  not  induce  failure  even  with  an  infinite  number  of 
repetitions  of  stress.  The  work  done  in  the  plastic  deformation  of 
metal  is,  then,  transformed  to  heat,  by  the  motion  along  the  slip- 
planes,  but  if  the  crystals  are  very  small  the  area  of  the 
boundaries  is  great  in  proportion  to  the  area  of  the  crystals,  and  fc 
the  stress  should  be  taken  up  by  the  elastic  boundaries  so  that  a 
greater  stress  -should  be  required  to  deform  the  crystal  and  thus  to 
induce  failure  under  repetition  of  stress.  If  the  composition  of 
the  crystals  is  such  that  they  have  the  same  resistance  to  deform- 
ation as  their  boundaries,  the  metal  should  not  fail  through 
fatigue  at  a stress  much  below  its  ultimate  strength.  If  the 
crystals  are  stronger  than  the  boundaries  the  larger  crystals  should 
be  stronger. 

As  to  the  evolution  of  heat  when  a metal  is  stressed 

repeatedly  above  its  endurance  limit,  such  a phenomenon  has  been 

observed.  Turner2'^  observed  it  and  Stromeyer0^  made  an  investigate . 

along  that  line,  while  Moore  and  Harsch  have  recentil  announced  a 

method  for  finding  the  endurance  limit  by  careful  measurement  of 

the  temperature  rise  for  stress  above  the  endurance  limit. 

Probably  there  is  some  heat  evolved  for  very  low  stresses,  but  the 

increase  when  the  endurance  limit  is  passed  indicates  the  truth  of 

the  assumption  from  the  evidence  of  the  pictures  and  the  hysteresis 

27 

experiments  of  Bair stow  , The  strength  of  the  crystals  relative 
to  their  boundaries  is  a varying  quantity  depending  upon  the 
material.  Professor  Moore  states  that  a troostitic  steel  which  was 
tested  had  an  endurance  strength  nearly  equal  to  the  elastic 
strength  and  that  very  pure  iron  had  the  same  property.  Troostite 
is  different  from  ferrite  in  almost  every  way  but  the  ratio  oi  the 


D- 


strength  of  the  boundaries  to  the  strength  of  the  crystals  is  the 
same,  the  strength  in  fatigue  should  be  the  same  proportion  of  the 
ultimate  strength  in  each  material.  Certain  impurities  tend  to 
segregate  in  the  boundaries  and  alter  the  strength  and  often  make 
the  material  "brittle."  Supposing  that  the  relative  strength  of 
the  crystals  and  the  boundaries  could  be  determined  ( and  it  should 
be  possible  to  strain  the  piece  on  the  microscope  and  determine 
whether  the  fracture  went  through  the  crystal  or  followed  the 
boundaries)  it  should  be  possible  to  determine  the  endurance 
strength  of  the  material  microscopically,  by  noting  the  areas  of 
crystals,  and  consequently  the  proportion  of  boundaries. 

For  a pearlitic  steel  with  comparatively  large  crystals  the 
increase  produced  by  doubling  the  area  of  the  average  crystal 
should  not  produce  a comparable  decrease  in  the  strength,  because 
the  proportional  area  of  the  boundaries  was  small  in  the  first 
place.  For  a sorbitic  or  martensitic  steel  the  difference  should 
be  considerable.  This  paper  is  concerned  only  with  a pearlitic 
steel  with  large  grain  size  throughout. 

V.  METHOD  OF  ATTACK. 

A.  Selection  of  Specimens. 

The  material  used  was  in  the  form  of  half-inch  rods  of  cold 
rolled  steel  containing  about  0*20%  carbon.  The  speciments  were 
thirteen  inches  long  and  were  designated  by  the  number  of  the  steel 
in  the  main  investigation  (52),  the  letter  assigned  a bar(  A,  B, 

C,  or  D),  and  a number  denoting  their  location  in  the  bar(0,  13,  28, 
39,  52,  65,  etc.).  For  example,  52A  104  was  the  piece  cut  from  bar 
A after  104  inches  had  been  cut  off  for  other  specimens. 


-17- 


Then  the  bars  were  arranged  as  they  were  originally  and  the 
specimens  for  the  three  series  of  tests  were  selected  so  that  any 
difference  due  to  difference  between  the  chemical  composition  of 
the  bars  would  be  balanced,  so  far  as  possible.  In  one  test  a 
specimen  from  A ran  out,  in  another  test,  one  from  B and  in  the 
third,  one  from  C.  The  first  two  were  from  the  end  of  the  bar  from 
which  they  came  and  the  last  from  the  middle.  Apparently  the 
location  did  not  have  a very  great  effect. 

B.  Method  of  Heat-Treatment. 

Trials  were  first  made  of  the  grain  size  that  could  be 
produced.  Small  pieces,  one  inch  long,  were  heated  in  an  electric 
ftirnace  to  varying  temperatures  for  varying  periods  of  time.  One 
series  was  normalized  by  heating  to  930°  Centigrade  fifteen  minutes. 
Another  was  heated  to  the  same  temperature  one  hour  and  another 
eight  hours.  During  the  one  hour  treatment  an  attempt  was  made  to 
learn  the  critical  points  of  the  steel  by  recording  the  temperatures 
during  the  heating.  The  temperatures  throughout  the  research  v/ere 
measured  by  means  of  a Pt  - PtRd  thermocouple  and  a potentiometer 
made  by  the  Pyrolectric  Instrument  Company.  It  was  calibrated 
against  a standard  noble  metal  thermocouple  and  checked  with  it 
during  the  year,  showing  that  the  two  had  not  changed  relatively. 
During  the  investigation,  also  a freezing  point  of  NaCl  was  found 
at  810°  Centigrade.  The  principal  use  of  the  instrument  was  to 
deep  the  temperature  constant  and  to  give  a rough  estimate  of  the 
actual  temperature.  It  was  sufficiently  accurate  for  the  purpose. 

The  trial  pieces  were  polished,  etched  with  a solution  of 
nitric  acid  in  absolute  alcohol,  4$  strength,  and  photographed  at 
a convenient  magnification  which  w&s  88  diameters.  The  treatment 


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-18- 


which  lasted  eight  hours  appeated  to  give  a very  marked  difference 
in  grain  size  and  twelve  of  the  thirteen  inch  rods  were  given 
that  treatment,  while  twelve  were  normalized.  The  fatigue  tests 
showed  that  the  series  with  the  lower  grain  size  had  a slightly 
lower  endurance  limit.  Therefore  a third  test  was  performed  to 
obtain  a still  larger  grain  size.  After  six  trials  one  was  found 
which  appeared  to  be  satisfactory  (121).  But  the  other  specimens 
had  been  heated  in  an  electric  furnace  which  could  not  be  used  at 
more  than  1000°  Centigrade  and  it  was  necessary  to  heat  them  in 
a coal  fired  muffle  furnace.  The  furnace  could  not  be  raised  to 
a'  higher  temperature  than  1100°  Centigrade  and  could  not  be 
maintained  long  at  that  temperature.  The  specimens  were  packed  in 
AlgOg  so  that  they  cooled  very  slowly  and  the  grain  size  developed 
was  fairly  large.  The  Equilibrium  Diagram  shows  the  location  of 
another  series  of  treatments  which  have  not  been  tested  but  have 
been  experimented  upon. 

C.  Testing  of  Specimens. 

The  endurance  tests  were  all  performed  in  machines  of  the 
type  designated  by  Mr.  F.  M.  Farmer  and  described  by  him  in  the 
Proceedings  of  the  American  Society  for  Testing  Materials  for  1919. 
The  stress  diagram  of  this  machine  is  shown  on  the  next  page  and  is 
little  more  simple  than  the  design  of  the  machine  itself.  The 
specimens  were  ground  to  size  and  then  the  central  section  was 
turned  down  to  a minimum  diameter  of  0 . 3 inch.  The  portion  removed 
was  a segment  of  a ten  inch  circle  so  that  there  would  be  no 
sudden  reduction  of  area.  The  machines  consisted  of  a bed  with  an 
adjustable  bearing  carrying  a pulley  and  half  a flexible  coupling 
at  one  end.  Four  short  sleeves  running  in  ball-bearings  were 


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placed  on  the  specimen.  Trunnions  of  the  two  end  bearings  support- 
ed the  specimen  in  the  machine  and  similar  trunnions  on  the  center 
bearings  supported  yokes  which  held  the  weights.  One  end  sleeve 
formed  the  other  half  of  a flexible  coupling  to  the  one  carried 
on  the  pulley-shaft  and  the  other  was  joined  by  means  of  a link 
to  the  reducing  gear  of  a revolution  counter.  The  specimen  was 
thirteen  inches  long.  The  centers  of  the  end  bearings  were  set  on 
marks  eleven  inches  apart  and  those  of  the  center  bearings  on 
marks  three  inches  apart.  The  weight  of  the  center  bearings  and 
that  of  the  weight  carrier  was  very  accurately  34  pounds  in  each 
case.  The  standardization  of  the  machines  made  it  possible  to 
use  any  machine  without  producing  discordant  results.  The  stress- 
es shown  in  the  tables  in  this  report  were  obtained  from  tables 
showing  the  diameter  of  the  specimen  and  the  unit-stresses  for 
loads  in  increments  of  five  pounds.  These  tables  have  bean 
checked  over  and  are  in  constant  use  in  the  laboratory. 

The  first  specimens  were  put  in  at  a stress  which  was  ex- 
pected to  break  them  in  a short  time.  The  machines  ran  about 
15C0  revolutions  per  minute  with  little  vibration.  The  soft  an- 
nealed specimens  were  easily  bent  and  had  to  be  set  very  care- 
fully. A slight  bend  or  excessive  vibration  appeared  to  have 
more  effect  than  any  difference  in  grain  size,  that  could  be  ob- 
tained. However  every  specimen  which  broke  or  cracked, failed  at 
the  minimum  section.  As  soon  as  a point  on  the  endurance  curve 
was  obtained  it  was  plotted  on  logarithmic  paper  posted  on  the 
wall  of  the  laboratory  for  convenience  and,  the  next  specimen 


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-19  a- 


Tlie  Farmer  Type  Reversed  Bending  Machine 
A is  the  specimen. 

B,  C,  D;  and  H are  'ball-bearings.  The  specimen  is  set  in  the 
sleeve  which  ruua  in  B.  Each  bearing  is  mo  tinted  with  trunnion 
pins,  whose  of  B are  set  in  a notch  and  the  pins  of  C,  D,  S are 
cantered  on  scratches  on  the  bar.  C and  D are  carried  by  A. 

H is  a flexible  coupling. 

K is  the  electric  driving  motor  and  pulley. 

M is  a yoke  connecting  the  yokes  supported  by  the  trunnions  of 

C and  D. 

N is  a revolution  counter  connected  to  the  specimen  by  a flat 
Imiidc  and  reducing  gear.  The  link  is  set  as  loosely  as  possible. 
W is  the  weight.  A frame  was  used  and  weights  hung  upon  it. 

C,  D,  M and  W with  the  connection  CD  and  the  spring  between  M an 
W weighed  thirty-four  pounds  within  a tenth  of  a pound.  The  W 
of  the  formula  in  the  diagram  following  this  page  is  equal  to 
half  the  total  weight. 


-19  id- 

stress  DIAGRAM  OF  FARMER  TYPE  REVERSED  BENDING  MACHINE 


Fj  8 


W1  = W2  = W3  = W4  = w 

X1  = Xo  = x 


The  moment  between  A and  B is  uniform  and  has  a maximum  value  ofWx 
The  beam  has  a circular  section,  but  the  section  AB  has  a radius 
turned  from  it  to  increase  the  fiber  stress  there. 

Maximum  fiber  stress  between  A and  B:  S = Mc/l=? 


Wx 

1/32  = d3 


Wx 

0.0982  d3 


Where 


stress 

bending 

distanc 


in  outer  fibers  lbs/ in 
moment  lb,-  in 
e from  neutral  axis= 


3 


d/2 

I = moment  of  inertia  of  section. 


-20- 

was  run  at  a stress  which  might  he  expected  to  cause  it  to  fail 
after  a certain  number  of  cycles.  The  point  lay  practically  in  a 
straight  line  until  the  number  of  cycles  approached  four  million 
when  the  line  became  horizontal,  indicating  that  the  specimen 
would  run  indefinitely  at  that  stress.  The  stress  at  which  a 
specimen  would  run  ten  million  cycles  was  designated  as  the  endur- 
ance limit.  The  machines  were  run  day  and  night,  continuously 
.until  the  specimen  broke,  striking  a trigger  which  caused  the 
switch  of  the  motor  to  be  opened  and  the  machine  stopped.  Then 
the  difference  between  the  initial  and  the  final  readings  of  the 
counter  gave  the  number  of  cycles  the  specimen  had  run.  According 
to  Basquin' s law^  S = K!Tm  where  S is  the  maximum  fiber  stress, 

N is  the  number  of  repetitions  necessary  to  cause  failu-  e,  and 
K and  m are  constants. 

D.  Study  of  Microstructure. 

One  specimen  from  each  test,  (52  C 104  and  52  D 0)  was 
photographed  microscopically  after  it  had  been  broken.  First  a 
longitudinal  section  of  the  section  of  greatest  stress  was  polish- 
ed, etched  and  examined.  In  each  case  it  showed  a banded  structure 
like  that  due  to  cold  working.  A cross-section  from  the  unstressed 
end  gave  a ground  for  comparison  of  grain-size.  A longitudinal 
section  from  the  unstressed  end  showed  very  mUch  the  same  banded 
structure  as  the  center  did  although  it  was  a little  less  pro- 
nounced. It  was  concluded  that  the  annealing  had  not  destroyed 
the  distorted  structure  due  to  the  original  cold-rolling  of  the 
steel . 


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-21- 

E.  Grain  count. 

A piece  of  ground  glass  was  fitted  to  a plain  glass  frame 
which  fit  the  back  of  the  camera,  the  magnification  changed  to 
100  diameter,  as  closely  as  it  could  be  obtained(and  maintained 
constant)  and  a circle  79.3  millimeters  in  diameter,  as  recommend- 
ed by  Zay  Jeffries,  was  drawn  upon  it.  It  was  much  easier  to 
count  the  crystals  upon  rhe  ground  glass  than  upon  a photograph 
because  it  was  always  possible  to  adjust  the  focus  so  that  a 
doubtful  line  could  be  identified  as  a grain-boundary  or  not,  but 
it  was  not  easy  to  make  an  accurate  count.  The  crystals  appearing 
within  the  circle  were  checked  off  by  means  of  a pencil  mark  on 
the  ground  glass.  Then  the  crystals  which  touched  the  circle  on 
either  side  were  counted,  their  number  divided  by  two  and  added 
to  that  of  the  crystals  wholly  inside  the  circle.  The  ground 
glass  was  then  removed  and  the  number  of  pencil  marks  counted. 

They  should  check  olosely  with  the  total  number  of  .grains  counted. 
If  they  did  not,  the  count  was  necessarily  repeated  from  the 
beginning.  After  a consistent  count  had  been  obtained  the  area 
was  photographed. 

The  series  which  had  been  heated  to  930°  C eight  hours 
lacked  uniformity.  The  best  explanation  that  can  be  found  is 
in  Carpenter  and  Elam’s  paper  on  "Crystal  Growth  and  Recrystalliz- 
ation in  Metals."  There  were  evidently  several  degrees  of 
stressed  grains, only  a few  had  been  strained  sufficiently  to 
grow  at  930°.  Most  of  the  crystals  had  been  strained  enough  to 
start  growth  at  1050°.  The  largest  crystals  in  the  eight  hour 
treatment  were  nearly  as  large  as  any  in  the  1050°  treatment  while 
the  smallest  were  like  the  smallest  in  the  fifteen  minute 


> 


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-22- 

treatment.  There  were  not  quite  so  man]/  small  crystals  but  they 
were  so  small  in  comparison  with  the  large  ones,  that  they  could 
not  be  imagined  as  influencing  the  properties  very  much,  thus  the 
grain-sizes  were  not  so  widely  different  as  they  would  appear  to 
be  in  the  pictures  nor  so  much  as  the  grain-count  would  indicate. 
For  this  reason  the  grain  count  is  not  to  be  trusted  in  all  cases. 
If  all  the  grains  are  counted,  and  the  attempt  was  made,  the 
results  are  somewhat  misleading  while  if  the  important  ones  only 
are  counted  a very  puzzling  distinction  is  introduced.  It  is 
rather  doubtful  whether  any  two  men  could  count  the  crystals  in 
a given  area  and  arrive  at  results  that  agreed  closely,  though 
the  accuracy  depends  largely  upon  the  type  of  structure. 

To  compute  the  area  of  the  average  grain:  A circle  of  73. 8mm. 

diameter  has  an  area  of  5000  square  millimeters.  The  magnification 
was  100  diameters.  Therefore  the  area  represented  by  the  circle 
was  5000/10000  or  0.5  mm2.  This  equals  500,000  square  rnicro- 
millimeters  or  "mu2".  Then  500, 000/ number  of  grains  counted  gives 
average  area  in  "mu2 11 . Table  IV  shows  the  results  of  the  count. 

A specimen  from  each  bar  used  in  the  test  of  each  series  was 
examined.  The  cross  -section  from  the  end  was  adopted  except  in 
the  case  of  53  C 33  where  a cross-section  from  the  center  was 
used  and  showed  no  great  variation  from  the  grain  size  of  52  C 52. 

VI.  CONCLUSION. 

The  endurance  limits,  found  by  means  of  the  Farmer  type 
reversed  bending  machines,  were  less  as  the  grain-size  increased 
but  this  difference  was  rather  small  for  the  steel  and  structure 


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-23- 

used,  and  not  sc  great  as  other  factors,  such  as  bending  previous 
to  the  test  and  vibration  in  the  machine. 

It  is  suggested  that  the  influence  -of  grain  size  depends 
upon  the  proportional  area  of  boundaries  to  crystals,  and  that  in 
the  steel  used  the  smallest  grain-size  contained  a small  propor- 
tional area  of  grain-boundaries  which  could  not  be  much  less  in 
the  largest  size. 

For  a higher  carbon  steel  with  a different  structure  or 
containing  different  impurities  the  difference  in  fatigue  strength 
due  to  grain  size  might  be  different,  due  to  a difference  in  the 
relative  strength  of  the  boundaries. 


-24- 

TESTS  ON  FARMER  TYPE  REVERSED  BENDING 

MACHINE 

TABLE  I 

0.2C % C, 

Cold-rolled 

steel, 

heated 

to  9 30°  C.  15 

minutes . 

Numb  er 

Dimensions 

Load 

Mch. 

Cycles 

Unit-s tr ess 

(inches) 

(lbs) 

(lbs/ins) 

52A52 

0.300 

50 

11 

54,200 

37,720 

52B39 

0.295(5) 

46 

11 

89,300 

36, 310 

52B26 

0.300(4) 

46 

11 

112,600 

34,700 

52G78 

0.295(5) 

43 

11 

250,600 

33,925 

52C26 

0.300 

44 

11 

271,300 

33,190 

52B13 

0.297- 

41 

11 

544,100 

31,879 

52G  0 

0.299 

41 

11 

624,100 

31,240 

52C104 

0.297(5) 

40 

11 

703,300 

30,945 

52B91 

0.298 

38 

11 

871,600 

29,250 

52A  0 

0.300 

40 

11 

1,183,200 

30,180 

| 52A104 

0.299(4) 

39 

11 

2,559,100 

29,718 

[ 52A143 

0.299 

36 

12 

10,719,700 

28,956 

TABLE  II 

Same  heated 

to  930°C  8 hours. 

Numb  er 

Dimensions 

Load 

Mch. 

Cycles 

Unit-stress 

' 52C91 

0.300 

54 

11 

500 

40,738 

1 52B104 

0.299 

51 

12 

2,800 

38,860 

! 52B78 

0.298 

49 

12 

79,800 

37,700 

52C13 

0.298(5) 

47 

11 

96,400 

35,995 

52A39 

0.300 

45 

11 

189,900 

33,948 

52B52 

0 . 299 

42 

11 

281,300 

32,000 

52A13 

0.297(5) 

40 

12 

829,400 

30, 789 (start., 

52A117 

0.297(5) 

35 

12 

1,082,100 

27>l5ent  at/ 

52A130 

0.299 

39 

12 

1,160,800 

29,718  ( star ■ i 

' 52A35 

0.299 

36 

12 

3,305,100 

27, 430b eh t a-, 

5 2D  0 

0.299 

37 

12 

3,307,900 

28,194 

52B  0 

0.297 

34 

12 

10,413,700  — 

28,400 

TABLE  III  Same  steel 

heated  to  1050°C. 

4 hours. 

Numb  er 

Dimensions 

Load 

Mch. 

Cycles 

Unit-stress 

52A91 

52A91 

0.301 

40 

12 

994,700 

29,877 

52B65 

0.298(5) 

37 

12 

2, 379,400 

23, 337 (start 

52C39 

0.299(5) 

35 

12 

3,002,000 

26,530bent  ao 

52CL2 

0.299(5) 

36 

12 

3,774,000 

27,295 

52A78 

0 . 300 

35 

6 

2,709,800 

26,400 

52C65 

0.293(5) 

34 

6 

10,861,400— 

26,040 

-25 


TABLE  IV 


Showing 

comparative  grain  sizes 

of  the  s 

pecimens  tests 

d. 

Humber  o 

f piece  Grains  in 

Area  of 

Variation 

Gr  oup . 

79.8mm.  circle  Grains 

( mus ) 

52A104 

580 

864 

7 

0.8 % 

52391 

593 

844 

13 

1.5$ 

Table  1 

52C104 

580 

864 

7 

0.8  % 

Mean 

584 

852 

1.5 % 

52A13 

407 

1228 

307 

20.0 f, 

52B52 

323 

1546 

11 

1.0$ 

Table  II 

52C13 

290 

1725 

190 

12.4% 

5 2D  0 

305 

1640 

105 

6.7 % 

Mean 

336 

15  35 

52A76 

189 

2645 

250 

8.6% 

52BS5 

189 

2645 

250 

8.6% 

Table  III 

52039 

161 

3110 

215 

7.5$ 

52C52 

157 

3180 

285 

9.9% 

174 

2395 

25 


Humber  52  A 104,  (xlOO) 
Grain  Area  - 864  mu8 
Unit  Stress  - 

29,718  ibs/lneh8 
Cycles  - 2,559,100 
Gross-section  from  end 


Humber  52  C 59,  (xlOO) 
Grain  Area  - 3110  mu8 
Unit  Stress  - 

26,533  id s/in ed 8 
Cycles  - 3,002,000 

(Bent  at  start) 
Cross-section  from  center 

Humber  52  D 0,  (xlOO) 
Grain  Area  - 1640  mu 8 
Unit  Stress  - 

28,194  lbs/inch8 
Cycles  - 3,807,900 
Cross-section  from  end 


■ m 1 
. 


36 


Humber  58  B 91,  (xlOO) 
Grain  Area  - 844  mu8 
Unit  Stress  - 

29,850  lt>  s/inch8 
Cycles  - 871,600 
Cross- sect ion  from  end 


Number  52  C 104,  (xlOO) 
Grain  Area  - 864  mu8 
Unit  Stress  - 

30,945  Its/ inch8 
Cycles  - 708,300 
Cross-section  from  end 


>* 


Number  52  B 52,  (xlOO) 
Grain  Area  - 1546  mu^ 
Unit  Stress  - 

32  j 004  lb s/inch8 
Cyci  S3  — 281,300 
Cross-section  from  end 


Number  52  A 13$  (xlOO) 

p 

Grain  Area  - 1225  mu 
Unit  Stress  - 

30,789  Ibs/inch8 
Cycles  - 829,400 
Cross-section  from  end. 

Number  52  C 13,  (xlOO) 
Grain  Area  - 1725  mu8 
Unit  Stress  - 

55,995  lbs/ inch8 
Cycles  - 96,400 
Cr  os  s — se  ction  from  end 


23 


Number  52  C 52,  (xlOO) 

p 

Grain  Area  - 3180  mu 
Unit  Stress  — 

27,995  lU s/inch 


Cycles  - 3 , 774,000 
Gross- sect ion  from  end 


Number  52  A 78,  (xlOO) 
Grain  Area  - 2642  mu2 
Unit  Stress  - 

26,4C0  Ibs/inch 
Gycles  - 2,709,800 
Cross-section  from  end 


29 


lumber  52  B 65,  (xlOO) 
Grain  Area  - 2642  mu-' 
Unit  Stress  - 

23 , 537  lb  s/inch-' 
Cycles  - 2,379,4-00 
Cross-section  from  end 


Number  52  B 65,  (xlOO) 
Not  used  for  grain  count 


Different  area  on  the 
same  surface  to  show 
unif  or  unity 


30 


Study  cf  two  Farmer  machine  specimens. 


Humber  52  D 0,  (x98) 
Cross-section  from 
end , un  str  e ssed 


Humber  58  C 104,  (x88) 
Cr o s s- s ac t i on  f r om 
end , un  str  e s sed 


31 


Humber  5£  L 0,  (xlOO) 
Longitudinal  section 
thr ough  end , wher  e 
moment  was  small. 
Banded  structure  due 
to  rolling. 


Humber  53  2 0,  (x38) 
Longitudinal  section 
t hr  ough  c ent  er , wher  e 
moment  was  at.  a 
maximum. 

Banded  structure 
longitudinal . 


Humber  5£  0 104,  (x88) 
Longitudinal  section 
through  center.  Maxi- 
mum stress. 


^timber  53  DO,  (xlOO) 
Longitudinal  area  through 
center  at  riagntfl  cation 
used  for  grain  count. 


Heat-  Treatments  of  Steel 
1.  0.80 /i  C,  cold-rolled. 

Number  13,  (x33 ) 

Heated  to  930  0 C 

One  hour 

Cooled  in  air 

Peer  li tic 


Numb  er  13,  ( x8  3 ) 
Heated  to  930?  0 
One  hour 

Quenched  in  water 
Sorbi  to-pear lite 


33 


Number  11,  (x°8) 
Heated  to  930°  C 
Fifteen  minutes 
Cooled  in  furnace 
Pear  15.  tic 
For  grain  size 


Number  14,  (x88) 
Heated  to  930°  C 
One  h^,ur 

Cooled  in  furne',ce 

Pear lit io 

For  grain  size 


Number  15,  (x38) 
Heated  to  930°  C 
Fight  hours 
Cooled  in  furnace 
Pear lit ic 
■por  grain  size 


■ 


34 


Humber  16,  (xlOO) 
Heated  to  1050°  C 
Four  hours 
Cooled  in  furnace 
Pear 11 tic 
For  grain  size 

Humber  1?  heated 
three  hours 

■'umber  18  heated 
tv;o.  hours 


Hu mb er  19,  ( xl 0 0 ) 
Heated  to  1050°  C 
One  hour 

Cooled  in  furnace 
Pear li tic 


For  grain  size 


5 5 


Number  ill,  (n!j.OQ) 
Heated  to  1150°  C 
One  n our  ( 3a  s-fur nac e ) 
Cooled  in  furnace 
( rnor  a raid  cooiii ig  i n 
the  furnace  used) 

Pear lit ic 
Por  grain  size 


ITumb  er  121 , ( xlOO ) 
Heated  to  1150°  C 
Pour  ncurs 
Cooled  in  furnace 
(Specimen  was  packed  in 
AI0O3  with  node e-metal 
thermo-couple  to  ensure 
even  tern  erature  and 
slow  cooling) 

Pear lit ic 
Por  grain  size 


8.  0.40  y£  C Steal 
Bars  8”  x 1" 

Utunber  31,  (x83) 

Heatad  to  900°  ^ 

Fifteen  minutes 

Cooled  in  furnace 

Pear litic 

For  grain  size 


Number  85,  (xlOO) 
Heated  to  1030°  C 
Two  hours 
Cooled  in  furnace 
Pear litic 
For  grain  size 


Number  85,  (x750) 

Same  as  above  but 
showing  peai  litic 
str  u c tur  e mor  e cl  ear  ly 


. 


37 


Humber  22,  (xlOO) 
Heated  to  9uOc  C 
with  Ho, 21,  23  &34 
Cooled  in  air 
Peariitic 


Humber  22,  (x500) 
Same  as  above 
8howing  tear  11  tic 
structure 


Humber  23,  (xl500) 
Heated  to  900°  C 
with  21,  28,  t 34 

Quenched  in  oil 
Sorb:'  tic . 


'"unbar  34,  (xlOO) 
Heated  to  900°  C 
Fifteen  minutes 
Quenched  in  water 
Troostitic 


■ u; lib  er  34,  ( xl 5 0 0 ) 
Same  as  above  showing 
details  of  structure 


I umb  er  8 8 , ( xl  C 0 ) 
Alloy  after  Carpenter 
And  Elam 
Sn  - 98.5  % 

SId  - 1.5  % 

Showing  manner  of 
growth  of  grains. 


Preparation:  Fifteen  grams  of  an  alloy  of  80  % Sn,  80  % 

So  were  melted  in  a crucible  and  185  grams  of  mossy  tin  were 
.*u.aed  and  x-he  melt  pour  m into  a chill.  A view  of  the  struct' re 
was  found  by  casting  on  plate  glass. 


59 


The  alloy  was  annealed  at  's00c  G one  hour  to  permit 
cornel ete  solution  of  antimen;  , polished,  etched  in(¥HglgS 
and  heated  thirty  minutes  at  800  c C.  The  crystals  turned 
brilliant  colors  and  the  advance  of  certain  crystals  at  the 
expense  of  others  could  be  traced  by  the  new  boundary  lines, 
showing  that  growth  takes  place  by  "boundary  migration,  not 
by  coalescence  of  crystals”.  An  attempt  to  repolishe  the 
piece  effaced  all  of  the  old  boundaries  and  left  the  surface 


unrecognl sable 


■ 


. 


■ 


j 

: 

J 

- 

- 

J 


001  06  SI  09  Sb  0£  SI  ? Z % % C 

A ’ A * 5 I < p %o 


—40- 

BIBLIOGRAPHY 

Books 

1.  Hibbard:  Manufacture  and  Uses  of  Alloy  -Steels,  (1904) 

2.  Johnson:  Materials  of  Construction,  Fifth  Edition,  Withey  and 

Ashton. 

3.  Merriman:  Mechanics  of  Materials,  8vo,  (1904). 

4.  Rosenhain:  Introduction  to  the  Study  of  Physical  Metallurgy 

(1915) . 

5.  Sauveur:  Metallography  and  Heat  Treatment  of  Iron  and  Steel, 

(1918) 

6.  Unwin:  The  Testing  of  Materials  of  Construction,  (1910). 

7.  Upton;  Materials  of  Cons  true  tic'll,  p.  109-118. 

Periodicals . 

8.  Andrews:  Engineering  80:  235-9,  534-8*  (1905) 

9.  Andrews:  Engineering  61:  91-2,  62:35,  68,  118,  (1896). 

10.  Bairstow:  Phil.  Trans.  Royal  Society,  210A:  35-55,  (1910). 

(Resume  in  Unwin,  p.  124-5) 

11.  Basquin:  Proc.  Am.  Soc.  for  Testing  Materials,  10:625.  (1910) 

12.  Carpenter  and  Elam:  Engineering  110:  325-9,424-6,486-90.(1920). 

13.  Eden,  xRose  and  Cunningham:  Engineering  92:  555-60,  693-8,(1911). 

14.  Ewing  and  Humfrey:  Phil,  Trans.  Royal  Society,  200  A;  225. 

(1902)  200  A:  241.  (1902). 

15.  Ewing  and  Rosenhain:  Phil.  Trans.  Royal  Society  195  A:  279-301. 

(1900) . 

16.  Farmer:  American  Machinist  51:  271-3.  (1913). 

17  Howard.  Proc.  Am.  Soc.  for  Testing  Materials  7:252.  (1907). 

18,  Joint  Committee  on  Fatigue  Phenomena  in  Metals: 


